Amply Regular Graphs with $b_1=6$

The unnoriented graph with $v$ verteces of valency $k$, such that every edge belongs to $\lambda$ triangles, is called an edge regular graph with the parameters $(v,k,\lambda)$. Let $b_1=k-\lambda-1$. In [1] it is proved that a connected edge regular graph with $b_1=1$ is either a polygon or a complete multipart graph all of whose parts have order 2. Edge regular graphs with $b_1\le5$ have been studied in previous work. In the present paper we investigate amply regular graphs with $b_1=6$.